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The blizzard may have ended Monday, but some Boston travelers whose flights were canceled because of the snowstorm may be stranded until Friday.

As the nor’easter that dumped as much as 18 inches of snow on the region in the past two days wound down yesterday, airlines that canceled hundreds of flights were scrambling to accommodate thousands of stranded travelers at Logan Airport and across the country. But some travelers were facing the prospect of being stuck in Boston for days.

“Recovering from a storm is a matter of putting the puzzle pieces back together — only it’s a three-dimensional puzzle that is constantly moving and shifting. We have to match pilots and flight attendants to available aircraft, in the right city,’’ said Mateo Lleras, a spokesman for JetBlue Airways, the largest carrier at Logan. The airline canceled 270 flights on Sunday and 300 more yesterday across the Northeast, and didn’t expect to be fully operational until midday today.

The delays and cancellations at Logan left passengers feeling helpless and exasperated by a system that appears to have no rhyme or reason as to which flights go and who gets on them.

“We’re just disappointed. . . . It’s been an emotional roller coaster ride since yesterday,’’ said Beth Burgess, whose family of four was scheduled to leave for a Kenyan safari Sunday night, but instead found themselves crisscrossing the terminals yesterday, trying to find a new route.

The Manchester-by-the-Sea family’s flight to New York was canceled, and then their Paris-bound Air France flight was called back to the gate due to a mechanical problem. As of yesterday afternoon, they had no idea when they were going to be able to leave. “I think everyone’s frustrated with each other,’’ Heather Burgess, 18, said of the scene at the airport.

There is a system behind getting planes back in the air, and back on schedule — it’s just a long and arduous process. And rescheduling stranded passengers is especially challenging during the busy holiday travel week when flights are full.

Airlines begin studying schedules days before a storm hits and cancel flights based on where the plane is coming from, where it’s heading, how many passengers have connections, and where the flight crews need to be.

“Trying to rebook passengers who have been canceled is a challenge for the airlines,’’ said Matthew Brelis, spokesman for the Massachusetts Port Authority, which runs Logan. On top of that, “If [airports] are having a hard time getting back on their feet, that means we won’t have planes coming here and we won’t have planes going back there.’’

Overall, the majority of yesterday’s flights taking off from Logan before 3 p.m. were canceled, and airport officials expected to be close to a normal schedule today. Still, airlines say it will take some time to accommodate all the stranded passengers.

Some travelers were left in limbo yesterday about when they might get a new flight. Teresa and James Sterling of Austin, Texas, spent Sunday night at Logan in a double bed fashioned out of two cots and were told they may have to wait until Thursday before they can get a flight home. So they watched their first blizzard from the massive windows next to their cots.

Jackie Adams, 28, a criminal defense lawyer based in Los Angeles, sat on a California-bound JetBlue plane for about 3 1/2 hours Sunday night — enough time for two rounds of deicing and two rounds of runway plowing before the plane was called back to the gate. As of yesterday, she didn’t know when she’d get another flight. “They did try,’’ she said of the efforts to launch the plane.

Airlines say it’s difficult to position enough flight crews in snowbound cities to make a return to a full schedule immediately following a storm, which means flights can still be delayed or canceled even when the sun is shining. Adding to that complication, pilots and flight attendants also have strict rules about how long they can fly, and they sometimes aren’t able to get to the airport at all when roads are icy and public transportation is limited.

A plane’s condition also goes a long way toward determining which flights get out. Planes due for maintenance are more likely to stay on track because they have to be sent to an airport that has the right mechanic to do the job, airline officials say. And airlines try to avoid parking planes overnight at airports hit by snow and ice to cut down on deicing times the next morning, so some planes flew into unaffected airports instead of flying into Boston, causing cancellations before and after the storm.

Virgin America, for example, canceled its Boston flights to San Francisco and Los Angeles yesterday evening and last night because it couldn’t get planes into Boston earlier in the day. “Because we have long hauls, we had to make the decision based on weather to not operate the inbound flights,’’ said spokeswoman Abby Lunardini.